CAIE A-Level Mathematics 1.5.1 Trigonometric Graphs

Practise sketching sine, cosine and tangent graphs in degrees or radians and reading amplitude, period, range, intercepts, extrema and solution counts after transformations.

Exam points

mark the correct period, intercepts and extrema before joining them with a smooth curve
derive amplitude, vertical shift and horizontal scale from a transformed trig equation
read ranges or count graph intersections only within the stated degree or radian interval

[Maximum number: 3]

Figure for Question 1.5.1—Trig graphs question 1 — CAIE A-Level Mathematics AS

The diagram shows the curve $y=k \cos \left(x-\frac{1}{6} \pi\right)$ where k is a positive constant and x is measured in radians. The curve crosses the x-axis at point A and B is a minimum point.

Find the coordinates of A and B.

State $\left(\frac{5}{3} \pi, 0\right)$ for point A

B1

Or exact equivalent.

Marking guidance:

Allow $x=\frac{5}{3} \pi$ or exact equivalent.

$x=\frac{19}{6} \pi$ for point B

B1

Or exact equivalent.
May be implied in coordinate or vector form.

y=-k for point B

B1

May be implied in coordinate or vector form.

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1.5.1—Trig graphs question 1